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First Steps in Linear Algebra for Machine Learning
Week 2
Week 2

- Video: LectureOverview of the second week
  . Duration: 1 minute
- Video: LectureFull rank decomposition
  . Duration: 8 minutes
- Lab: Scanned document processing
  . Duration: 30 minutes
- Quiz: Week 2
  12 questions

QuizQuiz • 30 min30 minutes

Week 2

Submit your assignment

Due DateMay 25, 2:59 AM EDTMay 25, 2:59 AM EDT

Receive grade

To Pass87% or higher

Grade

100%

We keep your highest score

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Week 2

Graded Quiz • 30 min

Due May 25, 2:59 AM EDT

Congratulations! You passed!

To Pass 87% or higher

Grade

100%

Week 2

Latest Submission Grade

100%

1.

Question 1

What is the rank of matrix ?

1 / 1 point

2

Correct

This matrix has 2 lineraly independent rows.

2.

Question 2

How many free variables does the system $Ax=0$ have, if $A=$

⎛ ⎝ ⎜ ⎜ 0 - 1 - 4 2213750 - 1 56 ⎞ ⎠ ⎟ ⎟

A = ⎝ ⎜ ⎛ 0 - 1 - 4 2213750 - 1 56 ⎠ ⎟ ⎞

?

1 / 1 point

1

Correct

3.

Question 3

Does the SLAE

- 8 x 1 - 5 x 1 - + x 2 2 x 2 3 x 2 + + + 5 x 3 7 x 3 8 x 3 = = = 102

have solution(s)? Use Rouche-Capelli Theorem.

1 / 1 point

Yes

No

Correct

Rank A = Rank (A|b)

4.

Question 4

What is the full rank decomposition of ?

1 / 1 point

Correct

5.

Question 5

What is the solution set for the system $Ax=b$ , where $(A|b)=\left($

- 3 5117 63 - 1 13 2 - 2 214 10 - 2 - 14 41011

\right)

(A ∣ b) = ⎝ ⎜ ⎜ ⎜ ⎛ - 3 5117 63 - 1 13 2 - 2 214 10 - 2 - 14 41011 ⎠ ⎟ ⎟ ⎟ ⎞

1 / 1 point

⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ - 1 6 + 1 6 x 4 1 9 - 10 9 x 4 5 18 - 5 18 x 4 x 4 ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ 1 50 - 2 5 x 4 14 25 + 1 5 x 4 29 100 + 7 10 x 4 x 4 ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ - 1 50 + 2 5 x 4 14 25 - 1 5 x 4 29 100 + 7 10 x 4 x 4 ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ - 1 50 x 3 + 2 5 x 4 14 25 x 3 - 1 5 x 4 x 3 x 4 ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

Correct

6.

Question 6

What is the dimension of the solution set for $Ax=0$ if $A=$

⎛ ⎝ ⎜ ⎜ ⎜ 3 - 5 82 46 - 1 - 7 11312803 ⎞ ⎠ ⎟ ⎟ ⎟

A = ⎝ ⎜ ⎜ ⎜ ⎛ 3 - 5 82 46 - 1 - 7 11312803 ⎠ ⎟ ⎟ ⎟ ⎞

?

1 / 1 point

0

Correct

$n-rank(A) = 0$

7.

Question 7

What is the $x^0$ (arbitrary partial solution) of $Ax=b$ if $(A|b)=\left($

624 - 30 139 - 9 - 5 - 3 - 17 215 533 - 25 1 - 13 4 - 5

\right)

(A ∣ b) = ⎝ ⎜ ⎜ ⎜ ⎛ 624 - 30 139 - 9 - 5 - 3 - 17 215 533 - 25 1 - 13 4 - 5 ⎠ ⎟ ⎟ ⎟ ⎞

1 / 1 point

Correct

8.

Question 8

Do rows of form a Fundamental System of Solutions for

x 1 4 x 1 5 x 1 - 7 x 1 - + + - 2 x 2 4 x 2 14 x 2 10 x 2 + - - + 3 x 3 x 3 11 x 3 5 x 3 - + - 3 x 4 9 x 4 3 x 4 = = = = 0000

1 / 1 point

Yes

No

Correct

$A$ has two linearly independent rows, and the SLAE has the solution set of $dim$ $2$ . The rows are the solutions for the SLAE.

ˆ